Unformatted text preview: A chain of sports clubs is interested in which features to offer in a new location. The CEO of the
chain gathered data from existing clubs regarding the number of members, median income in the
area, whether the club had a pool, and when classes were offered (morning, afternoon, night, all day). A. Give the regression equation for predicitng the number of members a new gym will have.
B. Give the appropriate coefficient of determination.
C. Interpret the coefficient for median income.
D. Interpret the coefficient for night classes.
E. Is the model valid for prediciting membership at the 5% significance level?
F. Is income a useful predictor for membership? Alpha = .10
G. I s there a difference in membership between gyms that offer only morning classes
and those that offer classes all day? Alpha = .05
H. Give a 95% confidence interval for the coefficient for income.
I. Give a range of values for the mean membership of gyms that have a pool, medain income
in the surrounding area of $44, 880, and offer classes in the afternoon.
J. Give a range of values for the membership of a gym that does not have a pool, offers classes
in the morning, and has a median income in the surrounding area of $46,924.
K. Is multicollinearity a problem in your model? Justify your answer. A. Ŷ = ‐902.991 + 0.053 X income + 434.299 X pool + 253.203 X morning + 308.593 X afternoon + 405.066 X night
B. .953
C. Holding all other indpt variables constant, for an increase of $1 in median income, selling price will increase on avg by $.05
D. Holding all other indpt vars constant, a gym that offers night classes will have 405.066 members more on avg than one tha
E. Ho: β1 = β2= β3 = β4 = β5 = 0 Ha: at least one β not = 0
F = 62.360 pvalue = 3.26 E ‐7
There is enough evidence to conclude the model is valid for predicting membership.
F. Ho: β1 = 0 Ha: β1 not = 0 T = 10.955 pvalue = 6.85E‐7
There is enough evidence to conclude income is a useful predictor for membership.
G. Ho: β3 = 0 Ha: β3 not = 0 T = 1.092 pvalue = 0.300
There is not enough evidence to conclude there is a difference in memebership between gyms that offer only mo
H. 0.043 , 0.064
I. Predicted Values for New Observations
95% 1608.2 , 2864.4
J.
New Obs Fit SE Fit 95% CI 95% PI 1 2236.3 281.9 (1608.2, 2864.4) (1410.7, 3061.8)X
X denotes a point that is an outlier in the predictors. Values of Predictors for New Observations
New Obs income pool morning afternoon night 1 44880 1.00 0.000000 1.00 0.000000
K. No, there are no indpt variables that are highly correlated to each other. SUMMARY OUTPUT Regression Statistics
Multiple R 0.984347
R Square 0.9689391
Adjusted R S0.9534087
quare
Standard Error
240.43032
Observations
16
ANOVA
df
Regression
Residual
Total SS
MS
F
Significance F
5 18032708 3606541.7 62.389639 3.261E‐07
10 578067.41 57806.741
15 18610776 Coefficients
Standard Error t Stat
Intercept ‐902.9914 311.49941 ‐2.898854
income
0.0533947 0.0048738 10.955408
pool
434.29865 221.27685 1.9626935
morning
253.20343 231.79863 1.0923422
afternoon 308.59336 252.49215 1.2221899
night
405.06573 197.46469 2.0513325 P‐value
0.0158647
6.846E‐07
0.0780863
0.3002996
0.2496616
0.0673579 Lower 95%
‐1597.055
0.0425351
‐58.7369
‐263.2761
‐253.9942
‐34.91301 Upper 95%
‐208.9274
0.0642542
927.33421
769.68297
871.18093
845.04447 members income
pool
1258
32223
1479
34975
1480
43187
1701
44337
2014
52167
2271
57521
2615
58347
2632
60960
2737
62201
2810
67993
3563
68770
3765
81289
3792
83902
4069
84594
4393
86855
4787
88381 morning
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1 1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0 afternoon night
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0 0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1 pool
N
N
N
N
N
N
N
Y
Y
N
N
Y
N
Y
Y
Y n + 405.066 X night rice will increase on avg by $.053.
mbers more on avg than one that offers classes all day. tween gyms that offer only morning classes and those that offer classes all day.
New Obs Fit SE Fit 95% CI 95% PI 1 1855.7 138.9 (1546.1, 2165.3) (1237.0, 2474.4) Values of Predictors for New Observations
New Obs income pool morning afternoon night 1 46924 0.000000 1.00 0.000000 0.000000 95% 1237.0 , 2474.4 Lower 95.0%
Upper 95.0%
‐1597.055 ‐208.9274
0.0425351 0.0642542
‐58.7369 927.33421
‐263.2761 769.68297
‐253.9942 871.18093
‐34.91301 845.04447 classes
morning
afternoon
night
morning
all
afternoon
night
all
all
morning
night
all
night
all
all
night ...
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 Spring '13
 Leffakis

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